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We demonstrate how a class of non-supersymmetric $SO(10)$ GUT with asymmetricleft-right theory $SU(2)_L \times U(1)_R \times U(1)_{B-L} \times SU(3)_C$ andPati-Salam theory $SU(2)_L \times SU(2)_R \times SU(4)_C$ as intermediatesymmetry breaking steps leads to successful gauge coupling unificationsatisfying proton decay constraints. The motivation behind this work is twofold: firstly to study the renormalization group evolution equations for gaugecouplings by keeping right-handed neutral gauge boson $Z_R$ around LHC energyrange leading interesting dilepton searches at collider while fixing chargepartner of the gauge boson $W_R$ at very high scale; secondly to explainneutrino masses and associated lepton number violating process likeneutrinoless double beta decay in three possible cases depending on how$SU(2)_L \times U(1)_R \times U(1)_{B-L} \times SU(3)_C$ breaks down to SM. Weinclude one extra fermion singlet per generation in order to implement gaugedextended seesaw where light neutrino mass is governed by natural type-II seesawmechanism whereas type-I seesaw contribution is exactly canceled out. Sincelight neutrino mass formula is independent of Dirac neutrino mass matrix, thevalue of Dirac neutrino mass is taken to be up-type quark mass matrix which isa characteristics of Pati-Salam symmetry relating quarks with leptons. Wepresent analytic relation for effective Majorana mass parameter andcorresponding half-life arising from new physics contributions due to purelyleft-handed currents through exchange of heavy right-handed neutrinos andsterile neutrinos. We numerically estimate effective Majorana mass parameterand half-life vs. lightest neutrino mass and derive lower bound on lightestneutrino mass by saturating with experimental bounds like GERDA Phase-II,KamLANDZen and EXO.

Neutrino Mass and Neutrinoless double beta decay in SO(10) GUT with Pati-Salam symmetry